Finding derivative question plz.... How should I find the derivative of y = x^(e^x)? I tried using the chain rule along with the power rule, coming out to: (e^x) (e^x) (X^(e^x - 1)) If I had took the natural log of both sides and then used implicit differentiation, I would have gotten as a derivative: (x^(e^x)) (e^x) (1/x + ln x) which is the correct answer according to my TI89. Why wouldn't the first method work? Or was there any flaw? By the way I just started Calculus as a high schooler.